A B757 Captain reported experiencing burning smell on departure along with a 'LEFT RECIRC INOP' warning message. They declared an emergency and returned to land at the departure airport.

Narrative

During climbout; at approximately FL240; the Purser called and reported a burning smell near the galley. After a brief discussion about the location the Purser said she would check further in the galley area. Within a few minutes she called again and said the smell was getting much worse and in her opinion it was electrical. While she was relaying this information the 'LEFT RECIRC INOP' light came on. We decided it was prudent to return to departure airport and told ATC of our desire. As we began turning around we began to detect the burning smell and donned our oxygen masks. We advised the Purser; Dispatch and the passengers that we would be going back. We asked ATC for the equipment to be standing by and declared an emergency. The descent and landing were normal and the smell began to dissipate as the overboard exhaust valve status message indicated it was open. After landing; emergency crews reported no smoke or heat from their infrared equipment. We taxied to the gate with the 'no cooling' horn on in the nosewheel well.